Project Summary: The objective of this proposal is to develop computationally ef?cient and theoretically sound multivariate statistical tools in the analysis of vast amounts of publicly available neuroimaging data. Translating raw neuroimaging data into brain connectivity networks is one crucial step towards understanding the brain. This proposal focuses on developing tools to construct brain connectivity networks for two types of functional magnetic resonance imaging (fMRI) data. The ?rst part of the proposal focuses on fMRI data collected under natural continuous stimuli. Conventional task-based fMRI experiments are performed under highly-controlled experimental settings, and such experimental settings are highly arti?cial and bear little resemblance to our real- life experience. To understand the central function of the human brain, new experimental paradigms have been developed to collect fMRI data under natural stimuli in real-life contexts such as watching a movie or listening to a story. The proposed research will provide new statistical tools to analyze these data and will advance knowledge of how brains process and share information. The second part of the proposal focuses on resting state fMRI data with potential unmeasured confounding variables. Most methods for constructing brain connectivity networks have assumed that there are no unmeasured confounders. However, this assumption is often violated in many data sets. Without adjusting for the unmeasured confounders, the estimated brain network will lead to spurious scienti?c conclusions. The proposed research will provide a novel method to address this particular issue. Finally, all of these methods will have open-source software. The proposed methods have applications well beyond neuroimaging data and are portable to other biomedical data such as genomics data and protein interaction data. The methods will be carefully evaluated via theory, simulation and data-based application evidence.